Dynamic Control of District Heating Networks with Integrated Emission Modelling: A Dynamic Knowledge Graph Approach Markus Hofmeistera,b,c, Kok Foong Leeb, Yi-Kai Tsaib, Magnus Müllerb, Karthik Nagarajanb, Sebastian Mosbacha,b,c, Jethro Akroyda,b,c, Markus Krafta,b,c,d,∗ aDepartment of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge, CB3 0AS, United Kingdom bCambridge Centre for Advanced Research and Education in Singapore, CARES Ltd., 1 Create Way, CREATE Tower #05-05, 138602, Singapore cCMCL Innovations, Sheraton House, Cambridge, CB3 0AX, United Kingdom dThe Alan Turing Institute, 96 Euston Road, London, NW1 2DB, United Kingdom Abstract This paper presents a knowledge graph-based approach for the dynamic control of a district heating network with integrated emission dispersion modelling. We propose an interoperable and extensible implementation to forecast the anticipated heat demand of a municipal heating network, minimise associated total generation cost based on a previously devised methodology, and couple it with dispersion simulations for induced airborne pollutants to provide automatic insights into air quality implications of various heat sourcing strategies. We create cross-domain interoper- ability in the nexus of energy and air quality via newly developed ontologies and semantic software agents, which can be chained together via The World Avatar dynamic knowledge graph to resemble the behaviour of complex systems. Furthermore, we integrate the City Energy Analyst into this ecosystem to provide building-level insights into energy demand and renewable generation potential to foster strategic analyses and scenario planning. Underlying calcula- tions use building and weather data from the knowledge graph in place of inherent assumptions in the official software release, facilitating a more data-driven approach. All use cases are implemented for a mid-size town in Germany as a proof-of-concept, and a unified visualisation interface is provided, allowing for the examination of 3D buildings alongside their corresponding energy demand and supply time series, as well as emission dispersion data. With this work, we outline the potential of Semantic Web technologies to connect digital twins for holistic energy modelling in smart cities, thereby addressing the increasing complexity of interconnected energy systems. Keywords: knowledge graph, digital twin, interoperability, energy modelling, emission dispersion 1. Introduction Climate change arguably poses humanity’s most formidable challenge, impacting almost every aspect of our lives [1, 2]. Recognising greenhouse gas emis- sions as its key driver, the transition towards a low- carbon future is widely acknowledged as a crucial im- perative [3, 4]. The decarbonisation of the energy sector requires significant changes, such as increased sector- coupling and greater penetration of distributed renew- able resources as well as the development of intelligent infrastructure and modelling approaches [5, 6, 3]. So- lutions for this inherently interdisciplinary transition re- ∗Corresponding author Email address: mk306@cam.ac.uk (Markus Kraft) quire holistic consideration of social, economic, envi- ronmental, and engineering factors across various geo- graphic and temporal scales [7]. Digital technologies like advanced metering infras- tructure, big data, machine learning, 5G, and the inter- net of things are increasingly recognised for facilitating cost-effective decarbonisation [8, 9]. The application of cyber-physical systems in energy research has grown significantly in recent years, often in the form of digital twins to explore optimal solutions for real-world prob- lems through the study of fully digital replicas [10, 11]. Digital twins can provide detailed digital representa- tions of assets, processes, or entire systems, describing their current state and how they behave over time and under different conditions and constraints. Digital twins have effectively addressed numerous real-world prob- Preprint submitted to Energy and AI May 8, 2024 lems [12]; however, the majority remains isolated from each other and lack interoperability due to differences in set-up, hardware or software, often stemming from individual funding initiatives or business interests [13]. Interoperability is defined as the ability of tools, sys- tems, and data to understand and use each other’s func- tionalities [14], and is essential to foster reusability of data and software assets and address cross-domain questions comprehensively and collectively [15]. For future energy systems, effective cooperation and coordi- nation beyond the ‘traditional’ energy sector are essen- tial to maximise synergies of increasingly intertwined systems, encompassing power generation, the built en- vironment, health, etc. A potential solution to this chal- lenge can be generalised in the form of connected digital twins - distributed collaborative entities that share data and computational capabilities to efficiently and effec- tively address complex questions [16]. It is anticipated that energy modelling will transition from single-institution models to distributed, collabo- rative approaches, allowing multiple domain experts to contribute [17]. Yet, integrating data across domains and resolving ambiguities while ensuring openness and transparency remains a widespread problem [18, 19]. Data are highly heterogeneous in both format and se- mantics, as different sources (i.e., sensors, texts, web, etc.) use individual formats (e.g., tabular data, geospa- tial data, natural language, etc.) [20]. Moreover, a lack of semantic interoperability can arise when cer- tain information is only known implicitly by domain experts or when the same concept might possess differ- ent meanings in different domains; however, an aligned understanding of models, assumptions, and data is piv- otal [1, 5]. O’Dwyer et al. [21] have demonstrated a sustainable energy management system to manage the flow of data between individual machine learning mod- els, districts, and cities; however a general and scalable solution for the construction of cross-domain models re- mains unrealised, impeding the ability to reproduce re- sults as well as adapt and combine existing models [18]. The World Avatar (TWA) project [16] creates an ecosystem that enables the transparent integration of heterogeneous models and data, thereby improving interoperability between various formats and soft- ware [22]. It leverages technologies from the Semantic Web stack to create a distributed dynamic knowledge graph, which by design is well suited to effectively ad- dress cross-domain questions. Ontologies provide un- ambiguous definitions of concepts and relationships to describe relevant data and computational agents. These agents act as executable knowledge components which render the graph inherently dynamic. They share a common worldview to ensure self-consistency and ac- complish tasks such as updating the graph, simulat- ing systems, or transmitting responses to the physical world. Agents can represent black box, grey box or physics-based models and can also wrap around ex- isting software or third-party application programming interface (APIs) to make them available semantically. With an initial focus on chemical and process engi- neering [14, 23, 24], TWA has evolved into a versa- tile tool to address decarbonisation questions in the en- ergy sector [25, 26, 22, 27], overcome cross-domain in- teroperability challenges in smart cities and city plan- ning [28, 29, 30, 31], and improve the resilience of complex systems [32]. Akroyd et al. [16] showed how a dynamic general-purpose knowledge graph based on ontologies and autonomous semantic agents is ideally suited to realising connected digital twins, e.g., to con- trol real-world assets, perform cross-domain simula- tions, or conducting geospatial and scenario analyses. The purpose of this paper is to provide a con- crete implementation example of how dynamic knowl- edge graphs can help to realise connected digital twins by combining previously isolated tools and data. The World Avatar is used to derive a more holistic energy perspective for smart cities by connecting (1) a knowl- edge graph-native receding horizon control for the heat generation of a district heating network with (2) emis- sion dispersion simulations to understand the impact of various heat generation strategies on air pollution and (3) detailed building energy modelling, by making the City Energy Analyst available semantically. The structure of this paper is as follows: Section 2 provides an overview of the current energy modelling landscape for cities, together with its challenges, and an introduction to The World Avatar dynamic knowl- edge graph. Section 3 develops new ontologies and soft- ware capabilities to address identified interoperability gaps using TWA. Section 4 highlights the results from the connected digital twin implementation and section 5 concludes the work. 2. Background Holistic smart city energy modelling encompasses a broad spectrum of considerations, from energy forecast- ing to generation optimisation as well as the assessment of potential consequences of proposed scenarios. This section provides an overview of previous research and the status quo in each of these fields. Each topic is introduced independently, following conventional com- munity practices; however, as depicted in Fig. 1, these 2 Figure 1: Towards holistic smart city energy modelling. Conventional approaches address relevant aspects like building energy, operations control, or air pollutant dispersion separately. Individual analyses, simulations, or optimisation often remain isolated, disregarding interdependencies and overlaps in their inputs and/or outputs. The World Avatar dynamic knowledge graph connects related data and computational agents, enabling unified and automated modelling based on a consistent world view. While input agents assimilate real world data into the graph, update agents act upon instantiated information. silos are resolved in the following sections using a dy- namic knowledge graph approach. Semantic Web tech- nologies and The World Avatar, which enable this inte- gration, are also introduced. 2.1. Energy system modelling for smart cities Energy systems are increasingly intertwined and de- mand a comprehensive approach to drive overall re- source efficiency and decrease emissions [4, 6]. They are closely tied to numerous key challenges of the twenty-first century, including security, affordability, and resilience of energy supply as well as socio- economic and environmental concerns, ranging from lo- cal air and water pollution to global sustainability initia- tives [7, 33]. A holistic energy system approach is im- perative to provide an efficient and reliable low-carbon energy supply, comprising the planning and scheduling of diverse energy carriers, such as electricity, gas, heat- ing, and cooling [12]. In this context, established methods to model en- ergy systems are being challenged by several emerging themes, as extensively discussed in the literature [17, 3, 2, 33]: increased sector-coupling and interactions be- tween energy vectors at various scales (e.g., from multi- national, national, community scale down to building level); rising flexibility of demand driven by new tech- nologies such as smart meters and load shifting; en- hanced integration of intermittent renewable resources, with the resulting need for more temporal detail; dis- tributed generation and an increasing share of pro- sumers, with the resulting need for higher spatial gran- ularity. With increasing connectivity, the ‘internet of energy’ has emerged as overarching paradigm to elim- inate waste in the power system [34], requiring mod- elling frameworks to optimise across scales, considering multiple spatial and temporal resolutions [7, 3]. Numer- ous studies have shown that artificial intelligence can help to improve grid performance and optimise energy distribution and control in integrated systems [35]; how- ever, interpretability of models and digital twins is also gaining importance [36]. A review of recent smart grid and digital twin efforts is provided by Sifat et al. [37]. A strong push towards open simulation and planning tools has been observed in recent years as vital building blocks for transparent modelling approaches that bridge scales and domains [12, 2]. While it has been demon- strated that open-source modelling frameworks and data platforms are often on par with proprietary or commer- cial models [3], impediments to interoperability persist due to technical and market barriers. Diverse require- 3 ments and limitations (e.g., regional scope) of individual tools, coupled with variations in applicability to specific problems and scenarios, pose a real challenge in inte- grating data and models [12, 38]. To address these chal- lenges, semantic approaches have been proposed, such as by Li and Hong [38], who developed a framework for grid-interactive efficient buildings which are responsive to grid pricing or carbon signals to achieve energy and carbon neutrality. 2.2. The City Energy Analyst The City Energy Analyst (CEA) is an established open-source computational framework for urban en- ergy system analysis [39], offering insights into build- ings’ overall energy demand, heating and cooling re- quirements, etc. as well as on-site renewable energy generation potentials. It has a global user base and has been applied to numerous case studies across the world [40, 41, 42, 43, 44]. The CEA toolkit comes with built-in databases, con- taining several assumptions required to run simulations. The databases include information about building prop- erties (i.e., OpenStreetMap (OSM) [45] building foot- print, height, and building usage) as well as environ- mental data such as weather and terrain [39]. Although this approach enables users to conduct simulations with- out the requirement for specific input data, the built-in assumptions may not always be representative. Priori- tising broad applicability over the integration of actual building-specific characteristics is a deliberate design choice, inherent to many top-down energy assessment tools. 2.3. Interoperability gaps Interoperability is the ability of different systems, de- vices, or applications to exchange and use information effectively and collectively. While technical interoper- ability within the energy sector is quite well-established, there is a need for more informational, functional, and business interoperability [20]. Fragmented platforms dominate the energy modelling landscape, with no uni- fied approach to harmonise data models or knowledge across all domains of the value chain [46]. This poses challenges for data integration, model validation, sce- nario comparisons, policy evaluation, and often re- sults in biased or subpar overall system performance, as decision-makers lack valuable information to assess certain cross-domain trade-offs or co-benefits of dif- ferent scenarios. Just to name two examples, cross- domain interoperability would allow studying the ef- fects of extreme weather events, such as heat waves, floods, storms, or earthquakes, on both the built envi- ronment and smart grid infrastructure, aiding in iden- tifying potential weak points and enhancing systemic resilience [32]. Secondly, emission analyses could ex- tend beyond the established assessment of overall green house gas emission amounts to explore detailed disper- sion patterns of individual air pollutants as the result of different energy provision strategies, by incorporating location and weather data. Current interoperability gaps can be addressed by adopting standards and frameworks to facilitate com- munication and collaboration among different mod- elling tools, stakeholders, and platforms or enhancing information exchange using common data models, on- tologies, and Semantic Web technologies [5]. While the first approach remains focused on the broader energy domain (e.g., by incorporating solar panels, battery stor- age, heat pumps, boilers and electric vehicles) [46], the latter one is in principle capable to connect seamlessly with any related domain, such as transport, agriculture and industrial production [47]. 2.4. Dispersion modelling Dispersion models can broadly be categorised as box models, Gaussian plume models, or advanced physical models [48, 49, 50, 51]. Given their popularity and abil- ity to incorporate a wide variety of input data [48, 49], e.g., complex terrains and buildings in the dispersion pathway, a Gaussian plume model is selected for this work, assuming that pollutant concentrations follow a Gaussian distribution. Specifically, AERMOD [52], a steady-state Gaussian plume model, also deployed by the United States Environmental Protection Agency to assess air pollution, is chosen due to available source code, good documentation, the support for multiple emission sources, and achievable input data require- ments (i.e., to ensure the availability of all required in- puts to run the model). AERMOD has been applied and validated for a wide variety of conditions: flat and complex terrains [53, 54, 55], various time scales [56] and emission sources, such as a cement complex [57] or a coal-fired power plant [58], and many more available in the literature. To account for the effect of buildings on the disper- sion of air pollutants, AERMOD incorporates a vali- dated downwash model to capture relevant turbulence effects [59]. 2.5. The World Avatar dynamic knowledge graph As introduced by Akroyd et al. [16], The World Avatar aims to create a digital ‘avatar’ of the world. 4 This vision of an all-encompassing world model is cur- rently worked towards using Semantic Web technology, following a general-purpose dynamic knowledge graph (dKG) approach [8]. The Semantic Web [60] is an extension of the World Wide Web with the aim of creating an interoperable ‘web of data’, making web content machine-readable by adding structured metadata. It builds on the use of ontologies and the Resource Description Frame- work (RDF) [61] for representing such metadata. An ontology provides an explicit description of a specific domain by formally defining relevant concepts and re- lationships between them. Due to strict formalisation, ontologies support unambiguous data sharing and reuse, and enable reasoning and inference of implicit infor- mation. Representing data using ontologies results in the formation of directed graphs, known as knowledge graphs (KGs), where nodes define concepts, instances, or data, and edges denote their relationships. KGs pro- vide extensible data structures well suited to represent arbitrarily structured data. Using Internationalised Re- source Identifiers (IRIs), KG resources can be uniquely identified, allowing data to be distributed across the web, while maintaining unambiguous links between en- tities. Such Linked Data [62, 63] supports FAIR data principles [15] and enhances the discoverability of in- formation. Knowledge graphs can be stored in triple stores, such as Blazegraph [64], which are designed to host RDF data in the form of subject-predicate-object triples. SPARQL [65] is a query language designed to interact with semantic information and can be used to query and update these stores. Beyond the capabilities of conventional KGs, such as DBpedia or Wikidata, TWA also includes semantically annotated computational capabilities, so-called agents, which operate upon instantiated entities and make the graph inherently dynamic [23]. Computational agents within TWA can be seen as executable knowledge com- ponents and perform diverse tasks, such as assimilating real-world data, performing calculations, updating the graph, or transmitting responses to the physical world. A derived information framework (DIF) [66] provides a KG-native solution to track data dependencies and manage information flow within TWA. Offering granu- lar data provenance on an instance level, it provides de- tails about the origin of any information and the agent responsible for its acquisition. By representing intrin- sic dependencies within the KG, the DIF enables au- tonomous data handling, allowing information to cas- cade across the graph. The combination of ontological descriptions, instan- tiated data, and autonomous agents makes TWA a pow- erful, extensible, and FAIR-compliant system for rep- resenting and reasoning about complex domains of knowledge. As everything is connected, the design sup- ports an interoperable ecosystem of connected digital twins (i.e., tools and services) to describe the behaviour of interconnected systems of systems. TWA is modular and scalable by design, supporting both decentralisation and interoperability across heterogeneous data sources and software. 2.6. Existing ontologies Within TWA, ontologies serve as modular compo- nents to represent and connect knowledge and data from different domains. Existing ontologies are reused where applicable, and new ontologies are proposed for identi- fied gaps. This approach honours existing domain ex- pertise and ensures compatibility with established com- munity understanding, while satisfying requirements of the provided data and target use case. After reviewing the literature, it became evident that relevant ontologies for the target use case are either not publicly available or do not adequately address the re- quired level of detail in the domain of interest: Al- though numerous ontologies have been proposed to rep- resent temporal concepts and/or time dependent mea- surements [67, 68, 69, 70], no efficient representation for large amounts of time series data could be identified. For utility network applications, available ontologies can capture detailed 3D topography, topology, and func- tional properties [71, 72, 73]; however, no conceptuali- sation for dynamic operations data to support the opti- mal coordination of district energy resources is publicly available [74, 75]. Ontology-based efforts to represent air pollution dispersion data exist [14, 23, 76], but lack compatibility with GeoSPARQL [77] for geospatial fea- tures, hindering their applicability to new locations; fur- thermore, a semantic solution for storing pollution con- centrations, often provided in raster format by mod- elling software, has not been devised [48, 49, 50, 51], a gap we aim to fill in this study. GeoSPARQL forms the de-facto standard for representing and querying geospa- tial data on the Semantic Web and provides an extension to the SPARQL query language for processing geospa- tial data. A more detailed review of previous ontology efforts is provided in supplementary material SM.2. 3. Implementation In this section we devise new domain ontologies and computational agents to operationalise real-world data related to the optimal control of a district heating sys- tem as well as the atmospheric dispersion of associated 5 air pollutants. The proposed agents exchange data and interact with one another via instantiated ontologies in the dKG, promoting a shared understanding among all actors. In contrast to conventional API-based methods, the explicit semantics of ontologically defined commu- nication establish a uniform, public, and well-controlled framework for expressing and interpreting data. This eliminates ambiguity in data representation, allowing agents to navigate and comprehend information consis- tently. 3.1. Ontologies Four new ontologies are proposed to represent time series data as well as relevant aspects of district heating network operations, emission dispersion and the build- ing energy domain. We adopt a bottom-up approach, with a primary focus on representing real operations data from our industrial partner, Stadtwerke Pirmasens, and capturing outputs from the City Energy Analyst. However, a sufficient level of generality is maintained to ensure reusability beyond the target use case. Reusing established ontologies maximises the benefits of pre- viously conceptualised domain knowledge and linked data, and requires the use of predefined concept and relationship names. Furthermore, typical naming con- ventions suggest the use of singular terms for concept names, relationships to be prefixed with ‘has’, camel case for composite phrases, among other field specific ones. The consistency of all proposed ontologies has been verified using the HermiT reasoner [78]. For a formal representation of the ontologies using description log- ics [79], please refer to the supplementary material. The codified [80] versions are publicly accessible on GitHub in OWL format: https://github.com/cambridge- cares/TheWorldAvatar/tree/main/JPS_Ontolog y/ontology. 3.1.1. Time series ontology This work elaborates an initial approach for a light- weight time series ontology [81], primarily to include a description of forecasts and how they have been derived. The key structure of the ontology is provided in Fig. 2. While SAREF’s extension [82] acknowledges that any entity (e.g., measurement) could be represented as either single value or time series, our approach consid- ers cases where entities also have associated time series forecasts. Hence, the domain of hasTimeSeries and hasForecast remains unconstrained. The Forecast concept is the central entity to represent any forecast and is associated with both a TimeSeries concept holding the actual predicted values and further meta data about the forecast to ensure proper provenance information. This includes the ForecastingModel used to derive the prediction, the length of the historical time series used for training and/or scaling, and the forecast hori- zon. Concepts from OM and the W3C time ontology are used to represent corresponding units and tempo- ral entities, such as the interval of the forecast horizon. The ForecastingModel concept captures key aspects of how forecasts are calculated, including the used train- ing TimeSeries to fit the model, potential covariates to be used when creating a forecast, and whether the data should be scaled when creating predictions (i.e., as required by many neural methods). Previously fit- ted models can be incorporated by specifying resolv- able URLs for both the saved model and checkpoint files (e.g., pickled pytorch models). Otherwise, default forecast models can be specified using a certain label. Further details on how the forecasting agent uses the ontology are provided in section 3.2.1 below. In con- trast to the SAREF extension [82], no explicit restric- tion on the frequency of the represented data is imposed; however, a Frequency concept is included, along with a resampleData property, indicating whether a time series needs to be resampled when creating a forecast (e.g., to comply with frequency requirements of certain forecasting techniques). 3.1.2. District heating network ontology This ontology aims to conceptualise district heating network operations and has been designed based on op- erational practices from Stadtwerke Pirmasens. While previous works often focus on static topology and 3D representations [72, 73], the shared information does not contain detailed geo-references to describe the grid structure (e.g., pipes, connectors). Moreover, the op- erations of the grid are rather dynamic, including cus- tomers’ heat demand and flow temperature profiles. As the work by Li et al. [75] is not publicly available for di- rect reuse, an ontology is proposed to capture essential aspects of district heating operations, leveraging some design choices from previous works. The three key concepts in the ontology are HeatingNetwork, HeatProvider, and HeatGenerator. The HeatingNetwork connects HeatProvider with Consumer instances to satisfy their HeatDemand (i.e., instantiated as time series). While the location of an individual Consumer presently remains undisclosed and is, hence, not explicitly modelled, any HeatProvider is connected to the grid via a GridConnection with observable properties. These properties include pressure as well as flow and 6 https://github.com/cambridge-cares/TheWorldAvatar/tree/main/JPS_Ontology/ontology https://github.com/cambridge-cares/TheWorldAvatar/tree/main/JPS_Ontology/ontology https://github.com/cambridge-cares/TheWorldAvatar/tree/main/JPS_Ontology/ontology ts:Forecast ts:hasForecast ts:hasForecastingModel ts:hasInputTimeInterval time:Interval ts:hasOutputTimeInterval ts:hasCovariate owl:Thing ts:TimeSeries ts:hasTimeSeries xsd:string xsd:string ts:hasRDB ts:hasTimeUnit ts:has TimeSeries ts:Forecasting  Model ts:hasModelURL rdfs:label om:Unit om: hasUnit ts:has Training TimeSeries ts:hasCheckpointURL ts:scaleData time:Duration ts:Frequency rdfs:subClassOf ts:resampleData xsd:boolean xsd:string xsd:boolean xsd:string xsd:string Concept Object property Data property Literal New / Re- used concept or relationshipColour coding: Figure 2: Time series ontology. The OntoTimeSeries ontology provides a light-weight representation for time series data within TWA. It further includes a general description of related forecasting concepts. Depicted labels denote existing/proposed concept and relationship names, with all referenced namespaces being declared in Appendix A. return om:Temperature, and provide insights into the temperature spread at these locations and, consequently, corresponding feed-in heat amounts. While the HeatProvider concept is kept gen- eral and represents any entity supplying heat to the grid, two subclasses relevant to the given use case are defined, namely MunicipalUtility and IncinerationPlant. The geospatial location of a HeatProvider is not explicitly modelled as part of this ontology. Instead, geo-references are established via links to corresponding building instances with detailed geometrical and geospatial information as part of the derivation markup as described in section 3.3 and illus- trated in Fig. 3. This approach keeps the OntoHeatNet- work ontology completely free of geospatial informa- tion, by reusing the capabilities of existing ontologies. An IncinerationPlant provides a certain ProvidedHeatAmount to the grid based on a sup- ply contract with the grid operator (for details refer to Fig. SM.1 in the supplementary mate- rial). A MunicipalUtility company can own multiple HeatGenerators, including conventional HeatBoilers and combined heat and power (CHP) GasTurbines. Each HeatGenerator is associated with a GeneratedHeatAmount and a corresponding ConsumedGasAmount concept, according to the gen- erator’s efficiency and used ocp:FuelType. Relevant costs are represented on both an individual generator and operator level. As CO2 emissions directly influence operating expenses (OPEX) due to emission certificate cost, they are modelled explicitly as part of OntoHeat- Network, while other air pollutants are conceptualised as part of OntoDispersion. Similarly, the electricity co-generation of a GasTurbine is captured, since respective revenue offsets heat generation OPEX. A detailed overview of the hierarchical cost structure and its components is provided in Fig. SM.2 in the supplementary material. An Availability concept is introduced to account for periods of plant shut-downs or required idle times of individual generators. Most properties will be instantiated as time series to ac- count for dynamic conditions (i.e., fluctuating prices, time-dependent heat demand) and to align with the hourly-resolved optimisation strategy applied by the municipal utility operator in the target use case. 3.1.3. Dispersion ontology This light-weight ontology aims to provide seman- tic markup for dispersion simulation data to create machine-readable inputs and outputs for agents and to foster cross-domain interoperability between various models. The key concepts of OntoDispersion are lo- cated in the bottom of Fig. 3, including their intended link to the OntoHeatNetwork ontology. A geospatial Scope concept specifies the simulation domain for the dispersion calculation and is defined as a subclass of geo:Feature to enable various geospatial querying and processing capabilities via GeoSPARQL. By using concepts from GeoSPARQL, the ontology is designed to be as robust as possible and easily extend- 7 OntoDispersion oh:Grid Connection OntoCAPE:hasPart oh:HeatProvider oh:hasUpstream GridConnection oh:hasDownstream GridConnection oh:Municipal Utility oh:Incineration  Plant oh:Heat  Generator OntoCAPE: isOwnerOf oh:HeatBoiler oh:GasTurbine om:Pressure OntoCAPE: Thermodynamic StateProperty oh:has ObservableProperty oh:Availability oh:hasOperating Availability oh:Generated HeatAmount oh:Provided HeatAmount oh:hasProvided HeatAmount oh:HeatDemand oh:has Heat Demand oh:suppliesHeatTo ocp:hasFuelType ocp:FuelType oh:CO2Factor oh:has CO2Factor oh:CostIn TimeInterval oh:has Consumed GasAmount oh:CoGen ElectricityAmount oh:hasCoGen ElectricityAmount oh:CoGenRevenue InTimeInterval oh:hasOperating Availability OntoCAPE: hasRevenue oh:provides HeatTo oh:has Generated HeatAmount om:Temperature oh:Consumed GasAmount oh:FuelUnitCost oh:hasUnitPrice oh:operates Concept Literal New / Re- used concept or relationshipColour coding: oh:Consumer oh:Heating  Network To be instantiated according to om or ts ontology disp:Static PointSource disp:Emission disp:emits Building IRI disp:has OntoCityGML CityObject disp:PollutantID disp:has PollutantID disp:NOx disp:PM2.5 disp:PM10 disp:Dispersion  Output disp:has PollutantID disp:z disp: hasHeight disp:Dispersion  Raster disp:hasDispersionRaster om:Height disp:Scope geo:Feature Object property Data property rdfs:subClassOfInstance OntoCAPE: hasCost Figure 3: Coupled heating network and dispersion modelling ontology. The OntoHeatNetwork ontology conceptualises the operations of a district heating network, while OntoDispersion provides a semantic description of air pollutant emission dispersion. Both ontologies can be linked through shared building instances to support geospatial emission analyses of district heating operations. Depicted labels denote existing/proposed concept and relationship names, with all referenced namespaces being declared in Appendix A. able to different areas. Versatile geospatial capabilities are essential to query which StaticPointSources, emitting one or more pollutant types, are located within a certain scope of interest. StaticPointSources link to corresponding building instances, which describe the actual geometries of the emission outlets. Each in- stance of DispersionOutput holds information on a set of raster data (DispersionRaster) for any ar- bitrary combination of pollutant type (PollutantID) and simulated height (z). In this work, we do not at- tempt to materialise raster data as RDF triples. Instead, any DispersionRaster instance simply provides the metadata (e.g., name of a GeoTIFF file) of a raster stored in an associated PostGIS database. Thus, an agent querying for dispersion raster data would obtain the metadata via a SPARQL query and perform a subse- quent SQL query to obtain the underlying raster values. 3.1.4. Building energy ontology Energy considerations are important in city master planning, and buildings are the main user of urban en- ergy. There are ontologies for urban building energy modelling [83, 84, 85] and master planning [28], but none really links the two fields. This ontology aims to bridge this gap to facilitate information exchange be- tween these closely related domains. An extract of the proposed OntoUBEMMP on- tology is shown in Fig. 4. The key concepts are dabgeo:Building, EnergyConsumption and EnergySupply, while the core building concept is shared with the OntoBuiltEnv ontology to facilitate interoperability between this energy-specific perspec- 8 dabgeo:Building bs:WallFacade bs:RoofFacade ub:SolarDevice ub:EnergySupply ub:Electricity Supply ub:HeatSupply ub:producesEnergy bs:hasFacade ub:Energy Consumption ub:Heating Consumption ub:Electricity Consumption ub:Cooling Consumption om:Energy ub:consumes Energy om:Areaub:hasSolar SuitableArea ub:hasTheo- reticalEnergy Production Concept New / Re- used concept or relationshipColour coding: To be instantiated according to om or ts ontology Object property rdfs:subClassOf ub:SolarCollectorub:PVPanel ub:PVTCollector Figure 4: Urban Building Energy Modelling and Master Planning ontology. The OntoUBEMMP ontology represents key concepts in the nexus of urban energy modelling and master planning, including building energy demands and solar potentials. Depicted labels denote existing/proposed concept and relationship names, with all referenced namespaces being declared in Appendix A. tive and a more comprehensive building description provided by OntoBuiltEnv. An EnergyConsumption concept is linked to its applicable building instance via a consumesEnergy relationship to represent a building’s energy demand. Renewable energy sources should be taken into consideration during master plan- ning to help offset EnergyConsumption. For exam- ple, a building can be equipped with SolarDevices on its bs:RoofFacade and its bs:WallFacade. For buildings with suitable areas for solar generation (i.e., hasSolarSuitableArea links to a non-zero area), the hasTheoreticalEnergyProduction relationship connects relevant areas with their potential Energy- Supply via the respective SolarDevice. There are different subclasses of EnergySupply, namely ElectricitySupply and HeatSupply, depending on the type of SolarDevice that could be installed. Instal- lation of PVPanel will generate ElectricitySupply, whereas SolarCollector will generate HeatSupply and the hybrid PVTCollector will generate both. The ontology uses OntoTimeSeries to instantiate Energy- Consumption and EnergySupply concepts as well as their subclasses to account for variable demand patterns or changing weather conditions. 3.2. Agents Several agents have been developed. An overview of all involved agents is provided in Fig. 5 and de- scribed below. All agents are packaged as individ- ual Docker services to foster distributed and platform- agnostic deployment (e.g., remotely in the cloud, as im- plemented for this use case). Compared to rather mono- lithic modelling approaches, the proposed design based on chained atomic agents allows for emerging complex- ity within system of systems architectures, without be- ing constrained to strictly linear dependencies. We were given actual historical operations data for a municipal district heating network of a midsize Ger- man town, Pirmasens. Based on this data, the district heating grid is instantiated per OntoHeatNetwork, us- ing 2020 historical time series data. Utilising the in- stantiated time series data, a forecasting agent can be used to predict any quantity, including the community’s HeatDemand. A district heating optimisation agent then generates a cost-optimised generator dispatch strat- egy to satisfy the forecast HeatDemand, considering both internal heat generators and sourcing from an ex- ternal waste incineration plant. The respective amounts of burned natural gas as well as heat from waste in- cineration are then converted by an emission estimation agent into corresponding NOx, PM2.5, and PM10 emis- sion streams. Together with the associated location in- formation, these emission streams form inputs to an dis- persion modelling agent to create a steady-state emis- sion dispersion map using actual historical wind data. All agents are implemented as derivation agents based on the DIF [66] and communicate directly via the dKG to ensure unambiguous provenance tracking of how a 9 loop optional optional The Word Avatar KGUser Opti- misation Trigger Agent AERMOD Agent DIF Fore- casting Agent Emission Agent Opti- misation Agent HTTP request with 1) Simulation start time 2) Optimisation horizon 3) Number of timesteps Update pure input instances to make existing derivations out-of-date (forecast, heat generation optimisation, emission and dispersion) KG updated Request update for dispersion derivation Check whether dispersion derivation still up-to-date Invoke agent to update derivation [for each timestep] Request update for emission derivation Check whether emission derivation still up-to-date Invoke agent to update forecast derivation Update outputs (heat demand and grid temperatures) KG updated Forecast derivation updated Invoke agent to update heat generation optimisation derivation Update provided and generated heat as well as consumed gas amounts KG updated Heat generation optimisation derivation updated Invoke agent to update emission estimation derivation Update emission instance KG updated Emission derivation updated Emission derivation up-to-date Update dispersion output KG updatedDispersion derivation updated Dispersion derivation up-to-date Optimisation run complete [if dispersion derivation out-of-date] Forecast derivation is out-of-date, causing heat generation optimisation and emission derivations to be both out-of-date [if emission derivation out-of-date] Figure 5: Agent interplay. Sequence diagram of all agents involved in the heat generation optimisation with integrated emission dispersion modelling (depicted for case of already instantiated derivation markups). certain output has been derived and which inputs it de- pends on. We introduce an optimisation trigger agent to coordinate between a user and the automated forecast- ing, optimisation, and subsequent emission dispersion simulation. While the dynamic load forecasting and supply-side optimisation use actual historical data, the City Energy Analyst agent can provide general insights into the en- ergy performance of buildings in case historical data is not available: utilising building-specific construction characteristics and weather data, various energy demand and generation profiles can be estimated. This com- plementary perspective provides valuable insights into building-resolved heat demands, e.g., relevant to anal- yse any potential extension of the district heating grid. 3.2.1. Forecasting agent This agent provides generic forecasting capabilities as part of TWA: it can retrieve instantiated time series, predict future values, and instantiate respective fore- casts back into the dKG using the OntoTimeSeries on- tology. Based on the Python library Darts [86], the agent supports forecasting via a wide range of meth- ods, ranging from classical white box models (e.g., es- tablished statistical methods such as autoregressive inte- grated moving-average (ARIMA) models and its deriva- 10 tives) to black box machine learning techniques (e.g., state-of-the-art transformer models), as well as grey box approaches such as Facebook’s Prophet [87]. The required input to derive any forecast comprise the instance associated with the time series to pre- dict, a ts:ForecastingModel describing the predic- tion model to use, the target ts:Frequency of the fore- cast to be created, a time:Interval denoting the tar- get forecast horizon, and a time:Duration denoting the historical data length to use for fitting and/or scal- ing of the historical time series data prior to creating the forecast. New forecasts are instantiated with relevant metadata, such as input and output time intervals as well as potentially applicable unit, as depicted in Fig. 2. The agent supports most forecasting models offered by Darts. The model to use is determined by the instantiated mark-up of the corresponding ts:Fore- castingModel instance in the dKG, with Prophet be- ing the default for arbitrary time series. Predictions with and without covariates are supported, depend- ing on whether ts:hasCovariate relationships are present for the target model instance. Additionally, custom models can be trained and stored within TWA for future forecasting. This involves creating custom ts:ForecastingModel instances with specific prop- erties, such as resolvable URLs for saved model files, relevant covariates, and scaling parameters. Thus, the agent offers both out-of-the-box forecasting capabilities and the flexibility to leverage custom fine-tuned models as needed. The agent can predict any arbitrary time series and is used to forecast heat demand and grid temperatures of a district heating network, using temporal fusion transformers (TFT) [88] in the context of the current work. Compared to many other deep learning methods, attention-based TFTs provide better explainability and interpretability thanks to insights into underlying atten- tion weights, which indicate what a model focuses on. The fitted TFT models are more accurate than the fine- tuned SARIMAX models deployed previously [89], es- pecially for longer forecast horizons. Further imple- mentation details as well as a detailed forecast perfor- mance comparison are provided in supplementary ma- terial SM.5.1. 3.2.2. District heating optimisation agent This agent leverages a previously developed optimi- sation routine to minimise total heat generation cost for a district heating provider [89]. The optimisation fol- lows a hierarchical approach based on merit-order prin- ciple to determine the OPEX-optimised short-term heat generation mix for a system comprised of multiple gas boilers, a CHP gas turbine as well as external heat sourc- ing from a waste incineration plant. This study show- cases the capability of dKGs in enabling connected dig- ital twins to derive more comprehensive energy perspec- tives and semantically integrates the existing model into TWA. The interested reader is referred to Hofmeister et al. [89], where the effectiveness of the optimisation has been demonstrated based on real-world operations data. While the initial optimisation relied on internally created SARIMAX predictions for key inputs, this agent increases modularity and fosters a micro-service architecture enabled through task-oriented connected digital twins by using externally instantiated fore- casts. The agent requires five ts:Forecast and one time:Interval instance to perform an optimisation. The interval specifies the optimisation horizon, describ- ing the period for which to derive the optimal dispatch strategy, while the five forecasts denote the forecasted oh:HeatDemand and four om:Temperatures (i.e., rep- resenting flow and return temperatures at the waste in- cineration and municipal heating plant) over this period, respectively. Besides these key inputs, further infor- mation are queried from the dKG during agent opera- tion. Upon successful optimisation, the following re- sults are instantiated back into the dKG according to the OntoHeatNet ontology: a oh:ProvidedHeatAmount instance describing the heat amount to be sourced from the waste incineration plant; an oh:Generated- HeatAmount and oh:ConsumedGasAmount instance for each gas boiler and CHP gas turbine denoting the heat amount to be provided and corresponding gas amount to be consumed by each heat generator, respec- tively; an oh:CoGenElectricityAmount instance de- scribing the amount of co-generated electricity by the gas turbine while providing the required amount of heat; an oh:Availability instance for each heat provider indicating its anticipated availability in the coming time steps. All optimisation outputs are instantiated as ts:Forecast instances for the respective concepts to not interfere with instantiated actual historical data. Newly created optimisation outputs automatically over- write previously instantiated ones. Upon first invocation of the agent, historical gas con- sumption, heat generation, and (if applicable) electric- ity generation data is queried to fit data-driven genera- tor specific gas consumption and co-generation models to be used during the optimisation. These models will be reused for all subsequent optimisation requests. The results of the agent implementation have been verified against previous optimisation results [89]. 11 3.2.3. Emission estimation agent This agent estimates the emission rates associated with heat production from burning natural gas (i.e., in gas boilers or the CHP gas turbine) or waste (i.e., in the waste incineration plant). For the time being, the assess- ment is limited to NOx, PM2.5, and PM10 as the major airborne emissions [90, 91, 92] and relies on literature- based emission factors instead of detailed combustion models for this proof-of-concept and due to the absence of detailed information on the waste incineration plant internals. Implemented as a derivation agent, all required in- puts need to be available in the KG. This includes one dh:ProvidedHeatAmount or, alternatively, one or more dh:ConsumedGasAmounts representing the (op- timised) time series for externally sourced heat or con- sumed gas amounts, respectively. A collection of con- sumed gas amounts resembles multiple gas boilers and gas turbines housed within the same building, emit- ting exhausts through a shared chimney. A disp:Sim- ulationTime marks the timestamp for which to esti- mate the emissions, i.e., for which later to simulate the emission dispersion. Lastly, a disp:StaticPoint- Source instance specifies the location at which the es- timated emissions will be emitted. During assessment, the time series values for pro- vided heat or consumed gas corresponding to the tar- get disp:SimulationTime are extracted. If multiple dh:ConsumedGasAmounts are given, their individual values are added together and processed collectively. Subsequently, emission factors are applied to convert the energy amounts into corresponding mass flow rates for NOx, PM2.5, and PM10, as required for the air pol- lutant dispersion simulation. The flue gas stream is treated as hot air, using typical values from the litera- ture. Please refer to supplementary material SM.5.2 for more details about the estimation methods. All outputs are instantiated according to the OntoDispersion ontol- ogy as disp:Emission instances with associated quan- tities for mass flow rate of pollutant as well as temper- ature and density of the exhaust stream. One emission instance per pollutant type is created. 3.2.4. Dispersion modelling agent This agent utilises AERMOD [52, 53] to simulate the dispersion of various air pollutants in a specific area of interest. It considers instantiated wind and emission stream data (i.e., mass flow rate, tempera- ture) from multiple point sources to generate emission concentration maps. Upon invocation, the agent per- forms three key steps: querying relevant inputs from the KG, executing AERMOD using this information, and finally instantiating the results back into the KG. As shown in Fig. 6, the key inputs are disp:Scope and disp:SimulationTime. The disp:Scope defines the polygon of the simulation domain (i.e., a rectangle) and disp:SimulationTime determines the time step of in- terest for which to run the dispersion calculation. Note that this input is shared with the emission estimation agent. The agent requires at least one instance of disp:StaticPointSource (e.g., a chimney emitting pollutants) that is located within disp:Scope to simu- late a plume. Instances of disp:StaticPointSource are not linked directly to dispersion derivations in or- der to facilitate future use cases involving mobile point sources (e.g., ships), which may move in and out of disp:Scope, making explicit markups very difficult to maintain. Instead, the agent uses disp:Scope to obtain relevant buildings and emission sources within the simulation area for the relevant timestamp. The disp:SimulationTime is also used to query the ac- tual (historical) weather data for that given time. Hav- ing retrieved all necessary information, the agent com- poses relevant input files and executes AERMOD. Sub- sequently, the agent processes the dispersion results into raster form and updates the disp:DispersionOutput time series instance in the dKG. Although we use AERMOD in this work, it could be swapped with any other dispersion model (e.g., EPISODE [93]) with minimal changes to the overall workflow outlined in Fig. 6. It is inevitable that a new agent would need to be developed; however, the pro- posed ontology would still suffice to represent relevant concepts (e.g., disp:DispersionRaster). 3.2.5. City Energy Analyst agent This agent calculates various aspects of a building’s energy performance using CEA as its simulation en- gine. To overcome limitations with built-in CEA as- sumptions, actual building stock data from the dKG are incorporated to allow for building-specific analy- ses, namely a building’s geometry and usage, the ge- ometry of surrounding buildings, weather, and terrain data. The implementation maintains CEA’s broad ap- plicability while adopting a building-resolved bottom- up approach. Upon invocation, the CEA agent attempts to retrieve the geometry of the target building(s) (i.e., specified by the building IRI(s) in the received HTTP request) as well as the geometries of the surrounding build- ings. Retrieved geometries from TWA replace CEA’s default OSM footprints. Subsequently, the agent will at- tempt to retrieve building specific usage data from TWA 12 to produce most meaningful energy consumption pro- files. After retrieving building level input data, the agent attempts to retrieve actual weather information at the target location from the dKG. Available local weather data supersedes CEA’s default behaviour of interpolat- ing weather information based on a few selected loca- tions within its own database. Lastly, the agent attempts to retrieve terrain data, specifically, the elevation of the land surrounding the target building(s) from TWA, to replace CEA’s default terrain input of a fixed elevation. Only a building’s geometry is strictly necessary for the agent to run successfully. In cases where other inputs cannot be retrieved from TWA (i.e., surroundings, us- age, weather, terrain), it proceeds to run CEA with its corresponding default assumptions. For details please refer to supplementary material SM.5.3. After running the simulations, relevant results are in- stantiated according to OntoUBEMMP in TWA. The various building energy demands (i.e., heating, cool- ing, electricity, grid) are instantiated as ub:Energy- Consumption instances. The agent also provides so- lar potential estimates for various types of solar gen- erators: PV panels, flat plate and evacuated tube solar collectors, and combined flat plate and evacuated tube PV-thermal collectors. These generators are instantiated as the corresponding subclasses of ub:SolarDevice, with their associated energy potentials instantiated as ub:EnergySupply entities. The suitable area for in- stalling solar devices is instantiated via the ub:has- SolarSuitableArea property. 3.3. Linked agents for cross-domain interoperability Individual agents are chained together via their input and output instances using TWA’s native derived infor- mation framework. This ensures that whenever a spe- cific piece of information is requested from the dKG, all dependent upstream inputs are scrutinised first to de- termine if they are still up-to-date or require updating before retrieval. We leverage this infrastructure to au- tomatically simulate associated air pollution dispersion whenever a new heat generation optimisation is com- puted and corresponding emission streams get instanti- ated. As illustrated in Fig. 5, the optimisation trigger agent acts as external input agent. To initiate an optimisation run, an HTTP POST request is expected, specifying 1) the optimisation start time, 2) the optimisation horizon (i.e., the number of time steps to be considered within each optimisation), and 3) the number of subsequent time steps to optimise in total. Upon receiving and veri- fying a request, the agent creates/updates corresponding instances within the dKG, and an update is requested from the dispersion modelling agent (also referred to as AERMOD agent due to the implemented model) via the DIF. The DIF then assesses whether an up-to-date dispersion instance already exists by comparing the in- stantiation timestamp of the derivation instance against the ones of corresponding inputs. If necessary, an up- date is requested, in which case the DIF works back- wards through the dependencies: dispersion simulations depend on emission estimation outputs, which depend on the heat generation optimisation, itself dependent on heat demand and grid temperature forecasts. The DIF initiates updates by invoking the associated agents, starting with the forecasting agent, responsible for the most upstream derivation, to ensure a proper cascade of all dependent information. Once all information is up-to-date, the initially requested dispersion outputs are simulated, which marks the end of the current optimisa- tion run. This loop is repeated until the number of time steps to optimise is reached. To ensure automated information cascading, deriva- tion markups need to be instantiated at the instance level, as illustrated in Fig. 6. It is important to note that this figure is a simplified representation for readability, with a more detailed diagram provided in Fig. SM.3 in the supplementary material. The optimisation trigger agent instantiates initial inputs for time:Interval, time:Duration, and ts:Frequency for each re- quested optimisation run (and updates them accordingly for subsequent time steps). Additionally, the agent pro- grammatically creates the depicted derivation markup if not already present and requests an initial assessment from responsible agents to generate corresponding out- puts for further markup. One derivation instance is created for each re- quired forecast, i.e., one oh:HeatDemand and four om:Temperature instances denoting the flow and re- turn temperatures at the municipal heat and waste in- cineration plant, respectively. The derivation outputs (i.e., updated ts:Forecast instances) are then collec- tively marked up as inputs to the heat generation op- timisation derivation. Given the accuracy of the fine- tuned TFT models, significant over- or underpredic- tions of required heat supply are improbable. Nonethe- less, the ‘network storage effect’ could offset such rare occurrences by utilising the network as short-term en- ergy storage. After optimising the generation dispatch based on the provided forecasts, multiple outputs are instantiated by the district heating optimisation agent, including one oh:ProvidedHeatAmount and several oh:ConsumedGasAmount instances, representing the time series of external heat provision from the waste in- cineration plant and gas consumption of several internal 13 time:Duration time:Interval Forecasting Agent Forecast derivation :isDerived From:isDerived Using ts:Forecast (grid temperature) ts:Forecast (heat demand) :belongsTo Heat generation optimisation derivation :isDerivedFrom DH Optimisation Agent :isDerived Using oh:Provided HeatAmount :belongsTo :isDerivedFrom :belongsTo Emission Agent :isDerived Using Dispersion derivation disp:Dispersion OutputAERMOD Agent :isDerived Using ts:Frequency :isDerivedFrom om:Temperature oh:HeatDemand ts:Forecasting Model oh:Consumed GasAmount oh:Generated HeatAmount Emission derivation disp:Emission either or (i.e., one derivation per forecast quantity) Agent Pure Input Instance Instances and relationships required by Derived Information Framework Output Instance Legend :belongs To disp:SimulationTime :isDerived From Request update and query om:MassFlow disp:Scope :isDerived From disp:StaticPointSource disp: emits :isDerived From om:has Quantity Figure 6: Derivation chain (simplified). Schematic depiction of knowledge graph native instance markup to resemble a model predictive control loop, coupled with automated air pollutant dispersion modelling. All referenced namespaces are declared in Appendix A, with not explicitly stated prefixes referring to OntoDerivation. heat generators, respectively. Subsequently, two individual emission derivations are marked up to account for different emission fac- tors used for waste and natural gas burning when es- timating associated emission rates. Different deriva- tion instances also account for different locations of the respective pollutant streams, as each derivation is de- rived from a disp:StaticPointSource, which intro- duces a geospatial reference to the dynamic optimisa- tion. The estimated disp:Emission outputs are used as source terms by AERMOD to simulate pollutant dis- persion maps. Although not explicitly marked up as 14 inputs, the agent requires at least one StaticPoint- Source (e.g., a chimney) within the disp:Scope of in- terest. The disp:SimulationTime instance represents the time for which to simulate the emission dispersion, and matches the first time step of the forecast and opti- mised heat generation. The district heating optimisation agent is designed to handle each optimisation request independently, i.e., without consideration of any preceding requests. The sole exception to this behaviour occurs when two con- secutive requests are an hour apart. In this scenario, the second request is treated as dependent on the pre- vious one, facilitating the tracking of relevant system state variables, such as cumulative profit from ongoing gas turbine activity. This enables a dKG-native receding horizon optimisation implementation, representing the first model predictive control-style application within TWA. While demonstrated for energy dispatch with in- tegrated emission modelling, similar derivation chains can automate various other (cross-domain) smart city workflows. Although the current implementation relies on an optimisation trigger agent as external input agent, this can easily be replaced with autonomous agents in the future. 4. Comprehensive energy perspective This section describes results and insights from the connected digital twin. Utilising the developed ontolo- gies and semantic agents, connected via the derived in- formation framework, allows for novel insights and ca- pabilities, such as 1) the knowledge graph-native con- trol of a district heating system, 2) the refinement of building energy analyses with latest instantiated build- ing stock data, and 3) cross-domain insights into heat generation induced air pollutants dispersion. The World Avatar offers a versatile visualisation in- terface to explore and interact with the underlying data, and supports both Mapbox (i.e., mainly for geographic information) and Cesium (i.e., mainly for detailed geo- metrical representations) as well-established visualisa- tion frameworks; however, it is crucial to understand that the presented visualisations are not the digital twin itself. Instead, the digital twins are a dynamic collec- tion of knowledge, data, and models embedded in the dynamic knowledge graph running in the background, with the visualisation being only one way to access it. Further options include a mobile app [94], virtual reality goggles, and a question answering system [95] besides a unified SPARQL endpoint. The integrated visualisation interface provides both map-based and (real-time) dashboard features. While map-based visualisations can help to understand the geospatial distribution of energy demand or the implica- tions of certain heat sourcing strategies on air pollution, dashboards focus on time series data and offer more de- tails about the current operational state of assets, such as the latest historical and forecast heat demand or the optimised generation strategy to satisfy it. 4.1. Resource-efficient heat provision The municipal district heating network has been in- stantiated based on actual data, including historical op- eration, weather, and market conditions. Operations data include details about the grid itself as well as at- tached heat providers, while market conditions cover electricity spot, gas, or CO2 certificate price time se- ries. Instantiated heating network data comprises the to- tal heat demand profile of all attached customers, opera- tional boundaries of the grid (e.g., minimum volumetric flow rate to ensure hydrodynamic stability), and connec- tion properties for the municipal heating and waste in- cineration plant, such as observed flow and return tem- peratures. Plant data includes information about the buildings hosting individual heat generators, along with their design characteristics (e.g., rated thermal power) and dynamic properties, such as time series of gener- ated heat and electricity as well as consumed gas. The integration across scales (i.e., from city level to de- tailed boiler specifications) as well as the inherent dy- namism due to the dKG-native control implementation combines and exceeds the capabilities of isolated energy system modelling and geographic information system- based approaches. Figure 7 presents a snapshot of the dynamic heat de- mand forecast dashboard. It shows the recent municipal heat demand history of all district heating consumers as well as the latest 24-hour demand forecast. The dash- board updates automatically with each new forecast, of- fering real-time insights into the latest operational state. In addition to time series visualisation (right), a gauge indicates the current state relative to operational/ob- served minimum and maximum values (left). Figure 8 illustrates the optimal dispatch of three con- ventional heat boilers, one CHP gas turbine, and exter- nal heat sourcing from the nearby waste incineration plant to satisfy the predicted demand (refer to Fig. 7). Currently, the demand of approximately 10.5 MW h is met through external sourcing and one heat boiler, while the remaining heat generators remain idle. Based on the projected demand as well as anticipated electricity spot prices, the CHP gas turbine is expected to be the main contributor to heat production as of in 4 hours, with mi- 15 Figure 7: Heat demand forecast. Dashboard view of the latest historical and forecast heat demand at any given time step. The historical load profile is shown left of the dashed line, with predicted values to its right. Figure 8: Optimised heat generation. Dashboard view of the cost-optimised heat distribution across generators and external sources, considering a waste incineration plant, three conventional gas boilers, and a gas turbine (based on forecast heat demand). nor support from the waste incineration plant and one additional gas boiler. 4.2. City energy analyses and scenario planning As actual (historical) energy data are not always available, an alternative approach is needed to estimate relevant quantities and gain insights on a broader scale, such as city level. The CEA agent provides estimates for various aspects of buildings’ energy performance, such as demands for different types of energy and on- site solar generation potentials. Compared to the of- ficial CEA toolkit, actual building stock (i.e., building geometry, geometry of surrounding buildings, property usage) as well as weather and terrain data are used for the underlying simulations (where available) to derive building-specific estimates. The outputs of the agent are 16 Figure 9: Visualisation of annual heating demand of each building simulated by the CEA agent. While map-based visualisation allows for quick identification of buildings with high/low heating demand, time series support the inspection of load profiles for individual buildings. instantiated and attached to the corresponding building in TWA and can be inspected via its unified visualisa- tion interface. Figure 9, for example, shows the an- nual heating demand for a selected neighbourhood in Pirmasens, allowing for a quick identification of build- ings (and areas) with high/low heating demand. Fur- ther simulation results, such as photovoltaic potential or gross-floor area specific values are provided in supple- mentary material SM.6. While Fig. 9 offers rather qualitative insights, the credibility of the results has been evaluated for both electricity consumption and on-site solar PV potential. The assessment compares instantiated agent results with actual historical consumption data or the official PV potential estimates provided by the state of Rhineland- Palatinate [96], respectively. By leveraging more gran- ular building an weather information from TWA, signif- icant accuracy improvements compared to native CEA (i.e., the unaltered CEA toolkit) can be achieved. The mean absolute percentage error (MAPE) relative to the above benchmarks could be reduced from 57.6% to 13.7% and from 28.1% to 12.9% for annual electricity consumption and solar PV potential, respectively. This improvement outlines the value of our bottom-up ap- proach to remove default assumptions in the underly- ing CEA toolkit where actual data is available from the dKG. Beyond cumulative annual figures, the CEA agent also provides both overall heat demand and solar poten- tial time series, which facilitate the assessment of pos- Figure 10: Heating load profiles simulated by the CEA agent. Heating demand and solar generation time series can be used to evaluate po- tential energy savings of on-site solar collector installations (depicted for a typical day in March). sible energy savings achievable with the installation of solar collectors. A basic analysis could explore utilising heat from rooftop solar panels to directly offset a build- ing’s heating demand, without factoring in any thermal storage. This simplistic assessment provides a prelimi- nary estimate for remaining heating demand from alter- native sources such as gas or district heating, together with the potential energy savings conferred by on-site generation (see Fig. 10). This capability can help to de- velop highly-granular heat maps of a city’s heating de- 17 (a) Heat generation related NOx emission dispersion as of 09 Dec 2020 06:00 UTC. (b) Heat generation related NOx emission dispersion as of 09 Dec 2020 07:00 UTC. Figure 11: Integrated emission dispersion simulation. The integrated simulation of heat generation induced air pollutants provides insights into air pollution implications of various heat generation/sourcing strategies, considering actual (historical) weather data. 18 mand (with or without considering on-site generation of solar energy), e.g., as currently required for the munic- ipal heat planning initiative in Germany. The building- resolved insights exceed the accuracy of most publicly available dataset, which are usually restricted to sim- ple raster maps with 50 × 50 m or 100 × 100 m reso- lution [97]. Combined with actual district heating grid location data, this information can be used to evaluate potential grid extension scenarios, both with regards to the total geospatially distributed heat demand as well as prevalent heat demand profiles considering actual build- ing usage patterns. 4.3. Impact on air quality Beyond insights into the energetic behaviour of build- ings and their optimised heat provision, a key strength of The World Avatar lies in generating cross-domain in- sights: Emission dispersion simulations are triggered automatically by each heat generation optimisation to immediately understand potential impacts of the pro- jected heat sourcing strategy, comprising multiple lo- cations, on the exposure of various parts of the sur- rounding population to associated airborne emissions. This proof-of-concept predominantly focuses on con- necting the dynamic cost optimisation with geospatial emission implications and a detailed investigation of po- tential health consequences remains yet unexplored. To mirror actual operating conditions, the dynamic optimisation is deployed with an hourly resolution. Hence, also the emission dispersion is simulated for each optimised hour, producing one instantiated disper- sion raster per air pollutant and elevation of interest. As generic Gaussian plume model, AERMOD supports various emission types; however, this work focuses on NOx, PM2.5, and PM10 as major pollutants (see sec- tion SM.5.2 in the supplementary material for details), with NOx typically exhibiting the highest proportional concentrations. While the dispersion at arbitrary ele- vations relative to the underlying terrain can be stud- ied, our focus centres on ground level (i.e., 0 m of el- evation), given its importance for pedestrians and the general public. A summary of relevant parameters for the AERMOD simulations is provided in supplemen- tary material SM.1. Instantiated dispersion maps can be overlaid with buildings or population density data to inspect various aspects and potential implications of heat generation in- duced emissions. In Fig. 11, this capability is show- cased, displaying NOx emission values in conjunction with instantiated building stock, where the colours indi- cate the usage of properties, with blue representing pre- dominantly residential buildings. The figure illustrates a historical scenario across two consecutive hours, dur- ing which the start-up of the CHP gas turbine has been deemed profitable by the optimisation routine. Figure 11(a) illustrates a heat provision situation where the majority of heat is sourced from the waste incineration plant situated in the North of the town. Fig- ure 11(b) depicts the heat generation one hour later, in- cluding the active gas turbine located at the municipal heating plant in the Southern part of the town. Given the different geo-locations of various heat sources, dis- tinct exposure scenarios emerge based on the chosen heat provision strategy due to the incorporation of wind data. Despite similar wind conditions and comparable maximum concentrations, both situations exhibit signif- icantly different exposure potentials. In the first sce- nario, multiple residential buildings face relatively high NOx concentrations, whereas these areas are shifted to regions without residential buildings in the second sce- nario. Figure 12 depicts the exposure of the town’s popu- lation to additional air pollution for two different heat sourcing strategies by overlaying the dispersion visual- isation over the population density raster: Despite sim- ilar weather conditions, certain geographic areas expe- rience significantly different exposure. The strategy de- picted in Fig. 12(a) sources most of the heat from the waste incineration plant located at the outskirts, result- ing in relatively higher but more remote emissions. The strategy shown in Fig. 12(b) distributes heat sourcing more evenly between the two available sites, resulting in lower overall concentrations; however, the municipal heating plant’s plume affects central areas with higher population density. This trade-off shall be addressed in the future by coupling heat generation with poten- tial health implications for the surrounding population within a multi-objective optimisation framework. Beyond the sole map view, virtual sensors can be placed at arbitrary locations to study air pollution expo- sure over time. These sensors extract data from underly- ing raster files and display corresponding values as time series for the respective pollutant types in the visualisa- tion side panel, as illustrated in Fig. 13. The depicted emission profiles for different pollutants look similar due to deploying a Gaussian dispersion model. Results could not explicitly be validated against actual local air quality readings due to a lack of available historical data (i.e., sensor readings) within the area of interest. How- ever, given the numerous previous calibration studies of AERMOD, we believe that the derived values possess at least indicative meaning. Moreover, simulated val- ues align well with applicable emission thresholds (see Table SM.5 in the supplementary material) as well as 19 (a) NOx emission dispersion as of 10 Dec 2020 04:00 UTC (b) NOx emission dispersion as of 10 Dec 2020 17:00 UTC Figure 12: Emission exposure. The integrated dispersion simulation provides insights into the exposure of certain parts of the population to additional air pollutants as a result of heat generation. Illustrated for simulated optimisation results overlaid with the population density raster. Figure 13: Emission time series. Virtual sensors allow inspecting simulated emission concentrations for arbitrary locations of interest as well as time scales. published hourly and daily mean readings reported by the waste incineration plant operator [98]. While the current dispersion model is intentionally simplistic for this proof-of-concept, the workflow can easily accom- 20 modate more sophisticated models in future iterations without significant modifications. 5. Conclusions In this work, we demonstrate the capabilities of The World Avatar dynamic knowledge graph to create com- prehensive energy perspectives for smart cities, thereby bridging domains in the nexus of energy, the built envi- ronment, and atmospheric dispersion. We connect de- tailed energy analyses for individual buildings with dy- namic control of a municipal district heating system and simulation of associated emissions, all seamlessly inte- grated within one interoperable semantic system. We have extended the ontological coverage of The World Avatar with knowledge models to describe time series and forecasts, district heating network opera- tions, building energy characteristics, and air pollutant dispersion and leverage these ontologies to instantiate real-world data. We have developed multiple semantic agents to act upon the instantiated data and deploy them in a connected fashion to provide the proof-of-concept for the first model predictive control application within TWA. We have implemented a generic forecasting agent and use it as part of this knowledge graph-native reced- ing horizon optimisation to minimise the total heat gen- eration cost of a district heating network. The outputs of the optimisation are directly linked with an integrated emission dispersion model to understand the impact of various heat generation and sourcing strategies on air pollution. The showcased degree of interoperability and automation, spanning from energy forecasting to cost- optimal generator dispatch to airborne emission disper- sion, is enabled by the automated tracking of dependen- cies between various agent and data instances within the dynamic knowledge graph. Furthermore, the City Energy Analyst is made avail- able as part of TWA to provide valuable information about buildings’ energy demands and on-site genera- tion potentials with regards to solar energy. The devel- oped agent offers a flexible enhancement to the orig- inal CEA toolkit by utilising latest instantiated build- ing and weather data from the knowledge graph to re- duce the dependency on default assumptions; thus, pro- moting a data-driven bottom-up approach for compre- hensive energy assessments of building stock at various levels (e.g., building, district, and city level). This per- spective complements the dynamic generation optimisa- tion with a more strategic angle, relevant to analyse any potential expansion of the district heating grid to drive low-carbon heating solutions. This work shows that semantically linked agents of- fer great potential to resemble the behaviour of com- plex systems, address interoperability challenges holis- tically, and implement automatable cross-domain smart city workflows, even beyond the energy sector. This study primarily focuses on showcasing an implementa- tion example of this capability, placing less emphasis on quantitative analyses. By integrating real-world sensor data, the accuracy of deployed models, such as AER- MOD or the City Energy Analyst, can continuously be refined and, reversely, virtual sensors can easily be de- ployed to fill gaps in the actual sensor landscape with simulated readings, thereby creating a truly interoper- able and dynamic cyber-physical system of connected digital twins. Acknowledgements This research was supported by the National Re- search Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Techno- logical Enterprise (CREATE) programme. Part of this work was also supported by Towards Turing 2.0 un- der the EPSRC Grant EP/W037211/1. M. Hofmeister acknowledges financial support provided by the Cam- bridge Trust and CMCL. M. Kraft gratefully acknowl- edges the support of the Alexander von Humboldt Foun- dation. The authors express gratitude to the Stadt Pirmasens, especially mayor Michael Maas and his team, as well as the Stadtwerke Pirmasens, with Christoph Dörr and his team, for their invaluable collaboration and generous support in sharing relevant data, enhancing the depth and quality of this research. This work also leverages data from©GeoBasis-DE/LVermGeoRP 2023. Further- more, the authors express gratitude to L.F. Ding and G.H. Xiao for their valuable contributions, particularly in sharing the Ontop mapping and engaging in helpful discussions. The graphical abstract leverages material designed by macrovector/Freepik. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. Nomenclature AERMOD AMS/EPA regulatory model (air dispersion model) API Application programming interface ARIMA Autoregressive integrated moving average 21 CEA City Energy Analyst CHP Combined heat and power DIF Derived information framework dKG Dynamic knowledge graph EEA European environment agency GeoSPARQL Geographic query language for RDF data IRI Internationalized resource identifier KG Knowledge graph LSTM Long short-term memory MAPE Mean absolute percentage error ME Maximum error NO2 Nitrogen dioxide NOx Nitrogen oxides OM Ontology of units of measure OPEX Operating expense OSM OpenStreetMap PM10 Particulate matter less than 10 µm in diameter PM2.5 Particulate matter less than 2.5µm in diameter PM Particulate matter PV Photovoltaics RDF Resource description framework RMSE Root mean square error SAREF Smart Applications REFerence ontology SARIMAX Seasonal autoregressive integrated moving average with exogenous regressors SMAPE Symmetric mean absolute percentage error SPARQL SPARQL protocol and RDF query language SQL Structured query language TFT Temporal fusion transformer TWA The World Avatar (dynamic knowledge graph) W3C World Wide Web Consortium WHO World Health Organization Declaration of Generative AI and AI-assisted tech- nologies in the writing process During the preparation of this work the authors used ChatGPT in order to enhance the readability and lan- guage of the manuscript. After using this tool, the au- thors reviewed and edited the content as needed and take full responsibility for the content of the publication. Data and code availability All the codes developed are available on The World Avatar GitHub repository: https://github.com/cambridge-cares/TheWorldAvatar. Developed ontologies can be found in the ontology sub- directory and instructions to reproduce the use case are detailed in the Pirmasens repository. Conflicts of interest There are no conflicts of interest to declare. Appendix A. Namespaces deriv: disp: oh: ts: ocp: OntoCAPE: OntoPowSys: ub: bs: contract: dabgeo: geo: om: owl: rdf: rdfs: time: xsd: References [1] O. Inderwildi, C. Zhang, X. Wang, M. Kraft, The impact of intelligent cyber-physical systems on the decarbonization of en- ergy, Energy & Environmental Science 13 (2020) 744–771. doi:10.1039/c9ee01919g. [2] L. Hofbauer, W. McDowall, S. 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